MarcelDv

I am not sure where this topic belongs, it is also posted in Science and Measurement...

Hi, i am quite new to the arduino and micro controller world, i have picked myself an project which is drivingme through the roof, and that is the Math around this.

The basics are an impact detection system using three 4 sound sensors and an Arduino Uno.My problem and honestly i might be over complicating this is as follow.

while drawing a possible scenario i realized that there is a few things i did not take into consideration while doing my programming..The problem i see, once i get an input on my first sensor (right Bottom ) Sensor 0,that sets the base for the rest of the calculations to happen.but at the moment the sensor is triggered there is already a set distance covered, meaning that the distance i calculate for sensor 1,2,3 will not be from the impact area, but rather fromA-1 B-2 and C-3 which leaves a big hole in my calculations.... smiley-cry

i have been looking at crating triangles from example 3-1-A to determine the XY Coordinate for A, the same for B and C....

Then using Equation of a Circle from 3 Points to determine the center point of the circle..

My problem is angels, i do not have any incoming angels to determine the XY of ABC...

Could anyone offer me a fresh approach to this, either better mathematical approach, or a different way i should be looking at this problem..

You need a minimum of 3 readings to determine the source, 4 increases your confidence.Typically you have a circle of uncertainty around each point, and where those circles intersect is the origin point.

How are you determining the distance from ABC to an impact point?With things like earthquakes, they work backwards using time.An event is known to have occurred.They know the time that each sensor first felt it. They know the time of the impact.They know (more or less) the speed of the wavefront thru water, rock etc.So (sensor_time - impact_time)/speed of propagation = distance away. There's your circle of uncertainty.Then do the math to find the intersection point.

You need a minimum of 3 readings to determine the source, 4 increases your confidence.Typically you have a circle of uncertainty around each point, and where those circles intersect is the origin point.

How are you determining the distance from ABC to an impact point?With things like earthquakes, they work backwards using time.An event is known to have occurred.They know the time that each sensor first felt it. They know the time of the impact.They know (more or less) the speed of the wavefront thru water, rock etc.So (sensor_time - impact_time)/speed of propagation = distance away. There's your circle of uncertainty.Then do the math to find the intersection point.

scjurgen

I don't think he got an impact time. The first signal that triggers is then defined as t=0. The others are delta values (so called TDOA) to the first dtn=tn - t etc. So, when you put up your equation of the circles, your radii of 3 circles will have an unknown delta in common for which you have also to resolve (resolve for x,y, and r). BTW, this problem is actually called multilateration http://en.wikipedia.org/wiki/Multilateration.

Based on timing and the speed of sound you have the length of line segments A1, B2 and C3. You want to find the point of impact in the center of the circle. Call the radius of that circle R. The distance of the impact from the four corners is 0:R, 1:A1+R, 2:B2+R, 3:C3+R. Write out the four equations and solve for the three unknowns: R, Xi and Yi (the coordinates of impact).

MarcelDv

I don't think he got an impact time. The first signal that triggers is then defined as t=0. The others are delta values (so called TDOA) to the first dtn=tn - t etc. So, when you put up your equation of the circles, your radii of 3 circles will have an unknown delta in common for which you have also to resolve (resolve for x,y, and r). BTW, this problem is actually called multilateration http://en.wikipedia.org/wiki/Multilateration.

That is correct, i do not have the impact time, i only have the first trigger on sensor 0, which is already and x distance from the impact point..

Also as to my initial line of thought, i do not have the incoming signal angle, which would help to solve the problem with triangle formulas.. so the next option

Thank you for the link, i will do some reading and see if i understand the principals of the multilateration

scjurgen

Also as to my initial line of thought, i do not have the incoming signal angle, which would help to solve the problemwith triangle formulas..

Just some food for thought , (not a solution for your current problem which has been addressed quite well by the previous post of johnwasser):

There is a technique to get an angle from an impact with 2 sensors using an... tada: artificial head. The mics are mounted in the ears. As the sound arrives at two different times, while one of them impacts directly you will have a slight phase shift from which you can determine a rough determination of angle (as long as you don't have sine sounds, which makes it complicate with high tones. Humans are quite good in this technique. the phase shift determination is done using autocorrelation functions, and this technique works also quite well in a noisy ambient.

Difference with the location problem is that the hyperbola defined by points AB and the one defined by points AC are 'orthogonal' - think of it as the red in the drawing rotated 90 degrees (make a drawing!!) There will be two intersection points and because the soundwave arrived first at A it becomes obvious which one to choose.

Also as to my initial line of thought, i do not have the incoming signal angle, which would help to solve the problemwith triangle formulas..

Just some food for thought , (not a solution for your current problem which has been addressed quite well by the previous post of johnwasser):

There is a technique to get an angle from an impact with 2 sensors using an... tada: artificial head. The mics are mounted in the ears. As the sound arrives at two different times, while one of them impacts directly you will have a slight phase shift from which you can determine a rough determination of angle (as long as you don't have sine sounds, which makes it complicate with high tones. Humans are quite good in this technique. the phase shift determination is done using autocorrelation functions, and this technique works also quite well in a noisy ambient.

Based on timing and the speed of sound you have the length of line segments A1, B2 and C3. You want to find the point of impact in the center of the circle. Call the radius of that circle R. The distance of the impact from the four corners is 0:R, 1:A1+R, 2:B2+R, 3:C3+R. Write out the four equations and solve for the three unknowns: R, Xi and Yi (the coordinates of impact).

Difference with the location problem is that the hyperbola defined by points AB and the one defined by points AC are 'orthogonal' - think of it as the red in the drawing rotated 90 degrees (make a drawing!!) There will be two intersection points and because the soundwave arrived first at A it becomes obvious which one to choose.